Satyaki is a very key warrior on the Pandava side. He is not just a relative of Krishna’s but also one of the most powerful Yadava chiefs, fully supporting Krishna in all his endeavours.
We see Satyaki fighting against all the top Kaurava warriors and holding his own easily. He also fights Alambusha the rakshasa, stopping his illusions with his divyastras. Bhishma, Drona, Karna all face his wrath at one time or another and on Day 12, he almost kills Karna. Karna is saved by the timely intervention of Duryodhana, Drona and Jayadratha. But who made this man such a great warrior?
Satyaki did not have one single guru; he had many of them. He was initially a student of Drona, Kripa and Bhishma and then later, Arjuna and Krishna. He had great devotion and affection towards his guru Arjuna and he demonstrated this on Day 14 when he went right into Kaurava lines to support Arjuna. We see that the Kaurava greats are all praise for Satyaki and exclaim how the sishya of Arjuna seems to be his equal in battle.
Satyaki being Drona’s sishya shows that it was not just the Hastinapur princes that Drona taught but also many, many others, who were not princes. This warrior also comes from the Yadu clan, which means he is of Suta origins too. Drona did not reject Sutas on the basis of their ‘varna’ either, as this shows.